Will you please work #20 in section 4, Test 1.

Sure! When you see percents, you should almost always think about plugging in 100. In this case, that works like a charm. Say the laptop originally cost $100. When it was put on sale for 20% off, the price went to $80. Buying an $80 laptop with 8% sales tax will cost . Which answer choice gives you 100 when you plug in 86.4 for *p*? Only choice D.

If you want to know WHY that works, then look at the algebra. Forget about the tax for a moment. Alma bought the computer at a 20% discount. So if the computer originally cost *x* dollars, then the price she paid can be calculated thusly:

Now we need to add 8% sales tax to that. We do that by taking the price she paid and increasing it by 8%:

That expression gives you the price Alma paid for the laptop—which the question calls *p*. So we can say:

Since the question asks you for the original price, *x*, in terms of *p*, solve for *x *by dividing.

## Comments (4)

Choice D is correct, not choice C, according to the official book

Yes–that’s true. I rushed this a bit and misread the question. I was treating p like it’s the original price, but p is the actual amount Alma paid. I will update the post to reflect the correct solution.

How can p=0.8x+(0.08)(0.8x) be rewritten as p=1.08(0.8x)

Think of it like this. Replace 0.8x with A. Then you’ve got A + (0.08)A.

A + 0.08A

1A + 0.08A

(1+0.08)A

1.08A

Then just substitute 0.8x back in for A.